10 citations · 16 across the 8 of their papers we have counts for
9 papers
Spanning solids and Murasugi sum in dimension four
Homayun Karimi, Seungwon Kim, Thomas Kindred +2
We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define…
Bridge position of 3-manifolds embedded in the 5-sphere
Román Aranda, Sarah Blackwell, Geunyoung Kim +2
We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and t…
Exotic definite four-manifolds with non-cyclic fundamental group
Robert Harris, Patrick Naylor, B. Doug Park
We construct infinitely many pairwise non-diffeomorphic smooth structures on a definite -manifold with non-cyclic fundamental group .
Doubles of Gluck twists: a five dimensional approach
David Gabai, Patrick Naylor, Hannah Schwartz
Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres with two minima are standard. Th…
Trisections of non-orientable 4-manifolds
Maggie Miller, Patrick Naylor
We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable…
Multisections of 4-manifolds
Gabriel Islambouli, Patrick Naylor
We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smoo…
Gluck twisting roll spun knots
Patrick Naylor, Hannah Schwartz
We show that the smooth homotopy 4-sphere obtained by Gluck twisting the m-twist n-roll spin of any unknotting number one knot is diffeomorphic to the standard 4-sphere, for any pa…
Trisection diagrams and twists of 4-manifolds
Patrick Naylor
A theorem of Katanaga, Saeki, Teragaito, and Yamada relates Gluck and Price twists of 4-manifolds. Using trisection diagrams, we give a purely diagrammatic proof of this theorem, a…
Testing bi-orderability of knot groups
Adam Clay, Colin Desmarais, Patrick Naylor
We investigate the bi-orderability of two-bridge knot groups and the groups of knots with 12 or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst a…